This site is supported by donations to The OEIS Foundation.



Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 4500 articles have referenced us, often saying "we would not have discovered this result without the OEIS".

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086792 Orders of finite groups G with the property that the sum of the orders of all the proper normal subgroups of G equals the order of G. 1
6, 12, 28, 30, 56, 360, 364, 380, 496, 760, 792, 900, 992, 1224, 1656, 1680, 1980 (list; graph; refs; listen; history; text; internal format)



The only Abelian groups with this property are the cyclic groups C_n where n is a perfect number, so this sequence can be seen as a groups analogy of perfect numbers.

Derek Holt (mareg(AT)mimosa.csv.warwick.ac.uk) computed the orders of the non-Abelian groups in the sequence up to n=500 and commented "In general, if 2^n - 1 is a Mersenne prime, then 2^(n-1)*(2^n - 1) is a perfect number and the group with presentation < x,y | x^(2^n-1) = 1, y^(2^n) = 1, y^-1 x y = x^-1 > has order equal to the sum of the orders of its proper normal subgroups." So if n is an even perfect number, 2n also belongs to this sequence (the numbers 12 and 56 above).


Table of n, a(n) for n=1..17.

Tom Leinster, Perfect numbers and groups

Tom De Medts, Attila MarĂ³ti, Perfect numbers and finite groups

Tom De Medts, Leinster groups

Sci.math, Groups analogy of perfect numbers


Cf. A000396.

Sequence in context: A249670 A009242 A032647 * A064987 A057341 A068412

Adjacent sequences:  A086789 A086790 A086791 * A086793 A086794 A086795




Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 04 2003


a(10)-a(17) added using "Leinster groups" link by Eric M. Schmidt, May 02 2014



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified November 30 04:46 EST 2015. Contains 264666 sequences.